Script from JKR's reading

[Ken Hutchinson]

No: HPFGUIDX 156843

--- In HPforGrownups at yahoogroups.com, puduhepa98 at ... wrote:
>
> > Nikkalmati:
> > I can't agree with your analysis of the respective  statements.
> > If"A is true, then B is not true."
> > From this statement  you cannot extract "If B is true, A is not true."
> 
> >Neri:
> You are  correct. This still leaves an alternative possibility "A is
> not true and B is  not true". However, here we have additional
> information: JKR also tells us  that B is true (that is, that
> Dumbledore *is* dead). This strikes down the  alternative possibility
> and therefore we are left only with "A is not true  and B is true"
> (that is, Snape isn't good and Dumbledore is dead). 
>  
> >Elisabet dusts off her mathematician hat)
> Er, nope. The statement "P  implies Q" *is* equivalent to "(Not Q)
> implies (not P)". 
> 
> 
> Nikkalmati: (not a mathematician so I am not sure the ramifications
of  using 
> "implies")
> Let me try an example:
> Proposed statement:  If A is a doctor, B did not die.
> Assuming B did die, does that prove A is not a doctor?
> No
> Of course, it is just as likely A is or is not a doctor.  We can't 
tell - 
> again JKR slips away.
> Nikkalmati
> 

No, Elisabet remembers her math very well, unlike certain authors! The
two relationships in your first comment above are a statement and its
contrapostive in the lingo of logic. IF the statement is true THEN the
cotrapositive is also true. Always.

In your doctor example the two relationships are again a statement and
its contrapositive. And you are correct, in this case the
contrapositive is not true. But neither is the statement. The laws of
logic are not being violated here. Unfortunately doctors are not able
to save every patient. The contrapositive of a true statement will
also be true. The contrapositive of a false statement will be false.
And it works in the reverse too. A statement and its logical
contrapositive are ALWAYS either BOTH true or BOTH false.

Ken